A) \[1.0\times {{10}^{-3}}\]
B) \[5.0\times {{10}^{-5}}\]
C) \[2.5\times {{10}^{-2}}\]
D) \[1.25\times {{10}^{-13}}\]
Correct Answer: D
Solution :
Radius of nucleus\[=1.25\times {{10}^{-13}}\times {{A}^{1/3}}cm\] \[=1.25\times {{10}^{-13}}\times {{64}^{1/3}}\] \[=1.25\times {{10}^{-13}}\times 4\,cm\] \[=5\times {{10}^{-13}}cm\] Radius of atom \[=1\overset{o}{\mathop{\text{A}}}\,={{10}^{-8}}cm\] Volume of nucleus/ volume of atom \[=\frac{(4/3)\pi {{(5\times {{10}^{-13}})}^{3}}}{(4/3)\pi {{({{10}^{-8}})}^{3}}}\] \[=\frac{125\times {{10}^{-39}}}{{{10}^{-24}}}\] \[=125\times {{10}^{-15}}\] \[=1.25\times {{10}^{-13}}\]
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